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Mathematical optimization problem restricted to integers
An integer programming, also known as integer optimization, problem is a mathematical optimization or feasibility program in which some or all of the variables
Integer_programming
Method to solve optimization problems
be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In contrast to linear programming, which
Linear_programming
Concept in integral mathematics
programming relaxation has a value differing from that of the unrelaxed 0–1 integer program. The linear programming relaxation of an integer program may
Linear_programming_relaxation
optimizer) a software package for linear programming, integer programming, nonlinear programming, stochastic programming, and global optimization. The "What's
List_of_optimization_software
Solving an optimization problem with a quadratic objective function
linear constraints on the variables. Quadratic programming is a type of nonlinear programming. "Programming" in this context refers to a formal procedure
Quadratic_programming
Software package
GNU Linear Programming Kit (GLPK) is a software package intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and
GNU_Linear_Programming_Kit
Datum of integral data type
for writing integer literals in many programming languages: Many programming languages, especially those influenced by C, prefix an integer literal with
Integer_(computer_science)
Computer arithmetic error
In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the
Integer_overflow
Optimization technique for solving (mixed) integer linear programs
cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not
Cutting-plane_method
Branch of mathematical optimization
problems on graphs, matroids and other discrete structures integer programming constraint programming These branches are all closely intertwined however, since
Discrete_optimization
Algebraic modeling language
among them: Linear programming Quadratic programming Nonlinear programming Mixed-integer programming Mixed-integer quadratic programming with or without
AMPL
Problem optimization method
Dynamic Programming in Macroeconomic Models." An introduction to dynamic programming as an important tool in economic theory. Dynamic Programming Explained:
Dynamic_programming
check convex hull (integer) affine hull integer projection computing the lexicographic minimum using parametric integer programming coalescing parametric
Integer_set_library
Subfield of convex optimization
Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified
Semidefinite_programming
Optimization by removing non-optimal solutions to subproblems
This approach is used for a number of NP-hard problems: Integer programming Nonlinear programming Travelling salesman problem (TSP) Quadratic assignment
Branch_and_bound
Optimization problem in mathematics
formulated as a quadratically constrained quadratic program. Since 0–1 integer programming is NP-hard in general, QCQP is also NP-hard. However, even for a
Quadratically constrained quadratic program
Quadratically_constrained_quadratic_program
Study of mathematical algorithms for optimization problems
transformed into a convex program. Integer programming studies linear programs in which some or all variables are constrained to take on integer values. This is
Mathematical_optimization
Mathematical combinatorial optimization method
combinatorial optimization for solving integer linear programming (ILP) and mixed integer linear programming (MILP) problems with many variables. The
Branch_and_price
Subfield of mathematical optimization
satisfaction problem Cutting stock problem Dominating set problem Integer programming Job shop scheduling Knapsack problem Metric k-center / vertex k-center
Combinatorial_optimization
Combinatorial optimization method
for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values. Branch
Branch_and_cut
Solution process for some optimization problems
that deals with problems that are not linear. Let n, m, and p be positive integers. Let X be a subset of Rn (usually a box-constrained one), let f, gi, and
Nonlinear_programming
Optimization technique
optimization approaches, such as algorithms from mathematical programming, constraint programming, and machine learning. Both components of a hybrid metaheuristic
Metaheuristic
Special case of discrete optimization
variables, rather than individual variables, as in ordinary mixed integer programming. Knowing that a variable is part of a set and that it is ordered
Special_ordered_set
example, a linear programming relaxation of an integer programming problem removes the integrality constraint and so allows non-integer rational solutions
Relaxation_(approximation)
Initial set of valid possible values
non-negative. In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible
Feasible_region
solutions, integer programming etc. Some versions of the map label placement problem can be formulated as multiple choices integer programming (MCIP) problems
Automatic_label_placement
Optimization problem in mathematics
rectangle packing problem for fixed sizes and orientations as an integer linear program. Further, constraints and variables can be added to minimize the
Rectangle_packing
Sequential model-based optimization of expensive black-box functions
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Bayesian_optimization
Matrix form in linear algebra
x} is restricted to have integer coordinates only. Other applications of the Hermite normal form include integer programming, cryptography, and abstract
Hermite_normal_form
Subfield of mathematical optimization
a convex quadratic function. Second order cone programming are more general. Semidefinite programming are more general. Conic optimization are even more
Convex_optimization
bases enable iterative solutions of linear and various nonlinear integer programming problems in polynomial time. They were introduced by Jack E. Graver
Graver_basis
Sequence of locally optimal choices
of a dynamic programming algorithm. Uriel Feige notes that: [Greedy algorithms] may be viewed as the ultimate form of dynamic programming, in which only
Greedy_algorithm
Graph with tight clique-coloring relation
closely connected to the theory of linear programming and integer programming. Both linear programs and integer programs are expressed in canonical form as seeking
Perfect_graph
Methods in numerical computation
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Rosenbrock_methods
Optimization problem
vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet
Vehicle_routing_problem
Extent to which a programming language discourages type errors
are not of the appropriate data type, e.g. trying to add a string to an integer. Type enforcement can be static (catching potential errors at compile time)
Type_safety
File format
(Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems. The format
MPS_(format)
Formula for systems of linear equations
prove that an integer programming problem whose constraint matrix is totally unimodular and whose right-hand side is integer, has integer basic solutions
Cramer's_rule
Optimization software package for linear programming
by IBM. The IBM ILOG CPLEX Optimizer solves integer programming problems, very large linear programming problems using either primal or dual variants
CPLEX
Algorithm used to solve non-linear least squares problems
proofs". Proceedings of the Jet Propulsion Laboratory Seminar on Tracking Programs and Orbit Determination: 1–9. Wiliamowski, Bogdan; Yu, Hao (June 2010)
Levenberg–Marquardt_algorithm
Algorithm for linear programming
"Simplex algorithms". In J. E. Beasley (ed.). Advances in linear and integer programming. Oxford Science. pp. 1–46. MR 1438309. Maros, István (2003). Computational
Simplex_algorithm
Optimization problem
Conforti, Michele; Cornuéjols, Gérard; Zambelli, Giacomo (2014). Integer Programming. Graduate Texts in Mathematics. Vol. 271. doi:10.1007/978-3-319-11008-0
Optimal_facility_location
Optimizing objective functions that have constrained variables
optimization Constraint satisfaction problem (CSP) Constraint programming Integer programming Metric projection Penalty method Superiorization Rossi, Francesca;
Constrained_optimization
Optimization algorithm
the Limited Memory Method for Large Scale Optimization". Mathematical Programming B. 45 (3): 503–528. doi:10.1007/BF01589116. S2CID 5681609. Malouf, Robert
Limited-memory_BFGS
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Gradient_method
Numerical optimization algorithm
(1973). "On Search Directions for Minimization Algorithms". Mathematical Programming. 4: 193–201. doi:10.1007/bf01584660. S2CID 45909653. McKinnon, K. I.
Nelder–Mead_method
File format for presenting and archiving mathematical programming problems
among them: Linear programming Quadratic programming Nonlinear programming Mixed-integer programming Mixed-integer quadratic programming with or without
Nl_(format)
Attribute of data
the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers
Data_type
Computer compiler optimization technique
|citeseerx= (help) A Tutorial on Integer Programming Archived 2009-09-05 at the Wayback Machine Conference Integer Programming and Combinatorial Optimization
Register_allocation
Class of logic puzzles
may be analyzed using graph-theoretic methods, by dynamic programming, or by integer programming. Let G = ( V , E ) {\displaystyle G=(V,E)} be an undirected
River_crossing_puzzle
Optimization algorithm
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization, also known as Lagrange-Newton method. SQP methods
Sequential quadratic programming
Sequential_quadratic_programming
Optimization method
target. However, some real-life applications (like Sequential Quadratic Programming methods) routinely produce negative or nearly-zero curvatures. This can
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Algorithms for solving convex optimization problems
programming". Dokl. Akad. Nauk SSSR. 174 (1): 747–748. Zbl 0189.19504. Karmarkar, N. (1984). "A new polynomial-time algorithm for linear programming"
Interior-point_method
Machine learning and inference framework
works use an integer linear programming (ILP) solver to solve the decision problem. Although theoretically solving an Integer Linear Program is exponential
Constrained_conditional_model
to implement than integer programming; however if a scoring function has pairwise contact potential included, dynamic programming cannot globally optimize
RAPTOR_(software)
Software for operations research
framework for solving mixed integer programs (MIPs) over heterogeneous networks. It can use CLP, CPLEX, XPRESS or other linear programming solvers to solve the
COIN-OR
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Generalized_iterative_scaling
Iterative method for minimizing convex functions
Atallah, CRC Press 1999, 31-1 to 31-37. V. Chandru and M.R.Rao, Integer Programming, Chapter 32 in Algorithms and Theory of Computation Handbook, edited
Ellipsoid_method
Numerical software
open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models. Written in C++ and published
HiGHS_optimization_solver
languages, programming languages, and problem-specific formats. Most of the linear programming, integer programming and nonlinear programming solvers accept
NEOS_Server
Optimization algorithm
forward–backward algorithm for monotone inclusions (which includes convex programming and variational inequalities). Gradient descent is a special case of
Gradient_descent
Solver for linear programs
software command line utility and library for solving linear programming and mixed integer programming problems. It ships with support for two file formats,
Lp_solve
Nearest integers from a number
returns the greatest integer less than or equal to x, written ⌊x⌋ or floor(x). Similarly, the ceiling function returns the least integer greater than or equal
Floor_and_ceiling_functions
American industrial engineer and mathematician (1938–2024)
to integer programming pioneered by Gomory. In particular, Johnson showed how the approach can be extended to the case of mixed integer programs. As
Ellis_L._Johnson
Numerical approximation algorithm
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Iterative_method
British mathematician (born 1945)
Wolsey is a Belgian-English mathematician working in the field of integer programming. His mother Anna Wolsey-Mautner was the daughter of the Viennese
Laurence_Wolsey
metaheuristic algorithms including the bat algorithm is given by Yang where a demo program in MATLAB/GNU Octave is available, while a comprehensive review is carried
Bat_algorithm
Decidable first-order theory of the natural numbers with addition
PA is in P, and this extends to fixed-dimensional parametric integer linear programming. Because Presburger arithmetic is decidable, automatic theorem
Presburger_arithmetic
Mathematical set closed under positive linear combinations
Integer Programming. John Wiley & Sons. pp. 88–89. ISBN 9780471982326. Conforti, Michele; Cornuejols, Gerard; Zambelli, Giacomo (2014-11-15). Integer
Convex_cone
Optimizer) is a software package for linear programming, integer programming, nonlinear programming, stochastic programming and global optimization. LINGO is a
LINDO
Computer benchmarking program
computing benchmark program developed in 1984 by Reinhold P. Weicker intended to be representative of system (integer) programming. The Dhrystone grew
Dhrystone
minimal set of integer vectors in C such that every integer vector in C is a conical combination of the vectors in the Hilbert basis with integer coefficients
Hilbert basis (linear programming)
Hilbert_basis_(linear_programming)
Cycle graph with all opposite nodes linked
Weismantel, Robert (2000). "Set packing relaxations of some integer programs". Mathematical Programming. Series A. 88 (3): 425–450. doi:10.1007/PL00011381. MR 1782150
Möbius_ladder
American businessman
"47-779 – Quantum Integer Programming – CMU Fall 2020". bernalde.github.io. Retrieved 2021-10-30. "47-779/785 – Quantum Integer Programming and Quantum Machine
Sridhar_Tayur
Linear programming algorithm
Application to Upper Bounds in Integer Quadratic Optimization Problems, Proceedings of Second Conference on Integer Programming and Combinatorial Optimisation
Karmarkar's_algorithm
Online database of integer sequences
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
German mathematician (1941–2014)
advisor was Egon Balas and his dissertation was titled Essays in Integer Programming. Afterwards he worked from 1971 to 1974 at the Berlin Science Center
Manfred_W._Padberg
Form of Newton's method used in statistics
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Scoring_algorithm
Type of algorithm for constrained optimization
Other nonlinear programming algorithms: Sequential quadratic programming Successive linear programming Sequential linear-quadratic programming Interior point
Penalty_method
Algebraic modeling language
linear programming (LP), mixed integer programming (MIP), and other related optimisation problems. It is a subset of the AMPL (A Mathematical Programming Language)
GNU_MathProg
General-purpose, object-oriented programming language
general-purpose, object-oriented programming language that adds Smalltalk-style message passing (messaging) to the C programming language. Originally developed
Objective-C
Method of solving linear programming problems
operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex
Big_M_method
Transportation and logistics optimization problem
rescheduling problem (VRSP) is a combinatorial optimization and integer programming problem seeking to service customers on a trip after change of schedule
Vehicle_rescheduling_problem
Combinitorics of Polyhedra
polytopes, whose vertices are subsets of a hypercube) arising from integer programming problems. A face of a convex polytope P may be defined as the intersection
Polyhedral_combinatorics
Mathematical algorithm for eliminating variables from a system of linear inequalities
03990 [cs.IT]. Schrijver, Alexander (1998). Theory of Linear and Integer Programming. John Wiley & sons. pp. 155–156. ISBN 978-0-471-98232-6. Keßler,
Fourier–Motzkin_elimination
American mathematician (born 1950)
Aix-Marseille University. His research interests include facility location, integer programming, balanced matrices, and perfect graphs. Cornuéjols graduated from
Gérard_Cornuéjols
Set of objects whose state must satisfy limits
(SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research focusing on the
Constraint satisfaction problem
Constraint_satisfaction_problem
Corporate planning method
obtained by optimization over more powerful mathematical programming models, usually integer programming models. While they acknowledge that the use of heuristics
Manufacturing resource planning
Manufacturing_resource_planning
Data types supported by the C programming language
of integer types <limits.h>. Rationale for International Standard—Programming Languages—C Revision 5.10 (PDF). p. 25, § 5.2.4.2.1 Sizes of integer types
C_data_types
Optimization algorithm
1016/0041-5553(66)90114-5. Frank, M.; Wolfe, P. (1956). "An algorithm for quadratic programming". Naval Research Logistics Quarterly. 3 (1–2): 95–110. doi:10.1002/nav
Frank–Wolfe_algorithm
sharing library. It has been used for solving continuous optimization, integer programming, and combinatorial optimization problems. It has been incorporated
Social_cognitive_optimization
Unsolved problem in computer science
problems in operations research are NP-complete, such as types of integer programming and the travelling salesman problem. Efficient solutions to these
P_versus_NP_problem
Optimization algorithm
convex problems by hill-climbing include the simplex algorithm for linear programming and binary search. To attempt to avoid getting stuck in local optima
Hill_climbing
Israeli mathematician
Israel Institute of Technology. He is known for his contributions to integer programming and nonlinear combinatorial optimization. Shmuel Onn did his high
Shmuel_Onn
purely integer, and mixed-integer nonlinear problems can be solved by the solver. Linear programming (LP), nonlinear programming (NLP), mixed integer programming
BARON
Technique for finding an extremum of a function
approximate the probe positions of golden section search while probing only integer sequence indices, the variant of the algorithm for this case typically
Golden-section_search
Notation for representing an integer in source code
In computer science, an integer literal is a kind of literal for an integer whose value is directly represented in source code. For example, in the assignment
Integer_literal
NP-hard problem in combinatorial optimization
Directed Graphs and Integer Programs", IBM Mathematical research Project (Princeton University) Dantzig, George B. (1963), Linear Programming and Extensions
Travelling_salesman_problem
Mathematical optimization software
(Mixed Integer Optimizer) is an integer programming solver which uses branch and bound algorithm. MINTO is a software system that solves mixed integer programming
MINTO
Local search algorithm
found during its execution. Fred Glover (1986). "Future Paths for Integer Programming and Links to Artificial Intelligence". Computers and Operations Research
Tabu_search
travel, tourism, insurance
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
travel, tourism, insurance